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On some control problems for heat transfer systems in perfused biological tissues. (English) Zbl 1140.49028

Summary: This paper considers the nonlinear optimal control governed by a bioheat transfer type model with Robin boundary conditions. The control estimates the blood perfusion rate and the heat transfer parameter on the boundary, which affect the effects of thermal physical properties on the transient temperature of biological tissues. The result can be very beneficial for thermal diagnostics in medical practices. The existence and the uniqueness of the solution are proved as well as stability under mild assumptions. Afterwards the optimal control problem is formulated. An optimal solution is proved to exist and, finally necessary optimality conditions are given. Several strategies for numerical realization based on the adjoint variables are provided.

MSC:

49N90 Applications of optimal control and differential games
80A20 Heat and mass transfer, heat flow (MSC2010)
92C30 Physiology (general)
35B37 PDE in connection with control problems (MSC2000)
49J20 Existence theories for optimal control problems involving partial differential equations
49K20 Optimality conditions for problems involving partial differential equations
93B30 System identification
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